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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard

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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard S-AES Encryption and Decryption S-AES Key Generation S-AES Encryption S-AES Decryption

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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard S-AES Encryption and Decryption S-AES Key Generation S-AES Encryption S-AES Decryption

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Simplified Advanced Encryption Standard  Simplified AES (S-AES) was developed by Professor Edward Schaefer of Santa Clara University in 2003  its purpose is educational, since its key and block size are very small 16bits  it is possible for students to encrypt or decrypt a block doing all operations by hand  it easier for students to understand the structure AES

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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard S-AES Encryption and Decryption S-AES Key Generation S-AES Encryption S-AES Decryption

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2 Round 1 Round 2

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Simplified Advanced Encryption Standard 16-bit Plaintext, P= D7 28 =1101 0111 0010 1000 16-bit Key, K= 4A F5 =0100 1010 1111 0101

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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard S-AES Encryption and Decryption S-AES Key Generation S-AES Encryption S-AES Decryption

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Simplified Advanced Encryption Standard , 16-bit Key Expand Key , Expand Key ,

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Simplified Advanced Encryption Standard , 16-bit Key Expand Key , Expand Key ,

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Simplified Advanced Encryption Standard  K= 4A F5 = 0100 1010 1111 0101  The input key, K, is split into 2 words, w0 and w1:  w0 = 0100 1010  w1 = 1111 0101

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Simplified Advanced Encryption Standard , 16-bit Key Expand Key , Expand Key ,

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Simplified Advanced Encryption Standard  S-AES Key Expansion

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Simplified Advanced Encryption Standard  Function g

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Simplified Advanced Encryption Standard , 16-bit Key Expand Key , Expand Key ,

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Simplified Advanced Encryption Standard  w0 = 0100 1010, w1 = 1111 0101  w2 = w0 ⊕ Rcon(1) ⊕ SubNib( RotNib(w1))  RotNib() is “rotate the nibbles”, which is equivalent to swapping the nibbles , Rcon is a round constant  SubNib() is “apply S-Box substitution on nibbles using encryption S-Box”  RotNib(w1) = 0101 1111  SubNib(0101 1111) = 0001 0111  Rcon(1) = 10000000 S-Box

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Simplified Advanced Encryption Standard  w0 = 0100 1010, w1 = 1111 0101  w2 = w0 ⊕ Rcon(1) ⊕ SubNib( RotNib(w1)) = 0100 1010 ⊕ 1000 0000 ⊕ 0001 0111 = 0100 1010 ⊕ 1001 0111=1101 1101  w2 =1101 1101  w3 = w2 ⊕ w1 = 1101 1101 ⊕ 1111 0101= 0010 1000  w3 = 0010 1000

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Simplified Advanced Encryption Standard , 16-bit Key Expand Key , Expand Key ,

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Simplified Advanced Encryption Standard  w2 = 1101 1101, w3 = 0010 1000  w4 = w2 ⊕ Rcon(2) ⊕ SubNib( RotNib(w3) ) = 1101 1101 ⊕ 0011 0000 ⊕ SubNib( 1000 0010 ) = 1110 1101 ⊕ 0011 0000 ⊕ 0110 1010 = 1110 1101 ⊕ 0101 1010 = 1011 0111  w5 = w4 ⊕ w3 =1011 0111 ⊕ 0010 1000 =1001 1111 S-Box

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Simplified Advanced Encryption Standard , 16-bit Key Expand Key , Expand Key ,

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Simplified Advanced Encryption Standard  Key  Key0 = w0w1 = 0100 1010 1111 0101  Key1 = w2w3 = 1101 1101 0010 1000  Key2 = w4w5 = 1011 0111 1001 1111

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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard S-AES Encryption and Decryption S-AES Key Generation S-AES Encryption S-AES Decryption

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Assume: P= 1101 0111 0010 1000  Key0 = w0w1 = 0100 1010 1111 0101  Key1 = w2w3 = 1101 1101 0010 1000  Key2 = w4w5 = 1000 0111 1010 1111

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 0  P= 1101 0111 0010 1000  Key0 = 0100 1010 1111 0101  R0= P ⊕ Key0 = 1101 0111 0010 1000 ⊕ 0100 1010 1111 0101 = 1001 1101 1101 1101

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  S-AES Encryption Round

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Simplified Advanced Encryption Standard  S-AES Transformation (Substitution and Shift row)

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 1 1) Nibble Substitution :  SubNib(1001 1101 1101 1101)= 0010 1110 1110 1110 2) Shift Row:  Swap 2nd nibble and 4th nibble  ShRow(0010 1110 1110 1110) = 0010 1110 1110 1110 S-Box

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Simplified Advanced Encryption Standard  S-AES Encryption Round

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  S-AES Transformation (Mix Column)

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Simplified Advanced Encryption Standard  Mix Column Table * 1 2 3 4 5 6 7 8 9 A B C D E F 2 2 4 6 8 A C E 3 1 7 5 B 9 F D 4 4 8 C 3 7 B F 6 2 E A 5 1 D 9 9 9 1 8 2 B 3 A 4 D 5 C 6 F 7 E

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Simplified Advanced Encryption Standard  Round 1 3) Mix Columns:  MixCol (0010 1110 1110 1110) = 0010 1110 1110 1110 ∗ 1 4 4 1 =  = 2 E E E ∗ 1 4 4 1 = (2∗1⊕E∗4) (E∗1⊕E∗4) (2∗4⊕E∗1) (E∗4⊕E∗1) * 1 2 3 4 5 6 7 8 9 A B C D E F 2 2 4 6 8 A C E 3 1 7 5 B 9 F D 4 4 8 C 3 7 B F 6 2 E A 5 1 D 9 9 9 1 8 2 B 3 A 4 D 5 C 6 F 7 E

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Simplified Advanced Encryption Standard  = (2⊕D) (E⊕D) (8⊕E) (D⊕E) = (0010⊕1101) (1110⊕1101) (1000⊕1110) (1101⊕1110)  (0010⊕1101) (1110⊕1101) (1000⊕1110) (1101⊕1110) = 1111 0011 0110 0011 = 1111 0110 0011 0011

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 1 4) Add round Key1  Key1 = 1101 1101 0010 1000  R1= Key1 ⊕ MixCol(ShRow(SubNib(R0))) = 1101 1101 0010 1000 ⊕ 1111 0110 0011 0011 = 0010 1011 0001 1011

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  S-AES Transformation (Substitution and Shift row)

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Simplified Advanced Encryption Standard  Round 2 1) Nibble Substitution :  SubNib(0010 1011 0001 1011)= 1010 0011 0100 0011 2) Shift Row:  Swap 2nd nibble and 4th nibble  ShRow(1010 0011 0100 0011) = 1010 0011 0100 0011 S-Box

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 2 4) Add round Key2  Key2 = 1000 0111 1010 1111  R2= Key2 ⊕ ShRow(SubNib(R1)) = 1101 1101 0010 1000 ⊕ 1010 0011 0100 0011 = 0010 0100 1110 1100 Ciphertext = 0010 0100 1110 1100

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Simplified Advanced Encryption Standard Simplified Advanced Encryption Standard S-AES Encryption and Decryption S-AES Key Generation S-AES Encryption S-AES Decryption

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Simplified Advanced Encryption Standard Shift Row Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Nibble Substitution Shift Row Add Round Key Nibble Substitution Add Round Key Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2 Round 1 Round 2

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Assume: C= 0010 0100 1110 1100  Key0 = w0w1 = 0100 1010 1111 0101  Key1 = w2w3 = 1101 1101 0010 1000  Key2 = w4w5 = 1000 0111 1010 1111

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Key2 = w4w5 = 1000 0111 1010 1111  C= 0010 0100 1110 1100  R0= C ⊕ Key2 = 0010 0100 1110 1100 ⊕ 1000 0111 1010 1111  =1010 0011 0100 0011

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 1 1) Inverse Shift Row  IShRow(R0)=IShRow(1010 0011 0100 0011)= = 1010 0011 0100 0011 2) Inverse Nibble Sub  ISubNib( 1010 0011 0100 0011 )= = 0010 1011 0001 1011 Inv S-Box

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard 3) Add Round 1 Key  0010 1011 0001 1011 ⊕ Key1 = 0010 1011 0001 1011 ⊕ 1101 1101 0010 1000 =1111 0110 0011 0011

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 1 4) Inverse Mix Columns :  MixCol (1111 0110 0011 0011) = 1111 0011 0110 0011 ∗ 9 2 2 9 =  = F 3 6 3 ∗ = (F∗9⊕6∗2) (3∗9⊕3∗2) (F∗2⊕6∗9) (3∗2⊕3∗9)  = (E⊕C) (8⊕6) (D⊕3) (6⊕8)  = (1110⊕1100) (1000⊕0110) (1101⊕0011) (0110⊕1000) * 1 2 3 4 5 6 7 8 9 A B C D E F 2 2 4 6 8 A C E 3 1 7 5 B 9 F D 4 4 8 C 3 7 B F 6 2 E A 5 1 D 9 9 9 1 8 2 B 3 A 4 D 5 C 6 F 7 E

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Simplified Advanced Encryption Standard  (1110⊕1100) (1000⊕0110) (1101⊕0011) (0110⊕1000) = 0010 1110 1110 1110 R1 = 0010 1110 1110 1110

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard  Round 2 1) Inverse Shift Row  IShRow(R1)=IShRow(0010 1110 1110 1110)= = 0010 1110 1110 1110 2) Inverse Nibble Sub  ISubNib( 0010 1110 1110 1110 )= = 1001 1101 1101 1101 Inv S-Box

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Simplified Advanced Encryption Standard Inverse Shift Row Inverse Mix Columns Add Round Key 16-bit Plain text 16-bit Cipher text Inverse Nibble Substitution Inverse Shift Row Add Round Key Inverse Nibble Substitution Add Round Key , 16-bit Key Expand Key , Expand Key , Round 1 Round 2

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Simplified Advanced Encryption Standard 3) Add Round 2 Key  R2= 1001 1101 1101 1101 ⊕ Key0 = 1001 1101 1101 1101 ⊕ 0100 1010 1111 0101 =1101 0111 0010 1000 Plaintext = 1101 0111 0010 1000 = D7 28

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